Moore's law is an observation made by Gordon Moore, co-founder of Intel Corporation, in 1965. It states that the number of transistors on a microchip doubles approximately every two years, while the cost of the chip is halved. Essentially, this means that computing power increases exponentially over time.
Moore's law is associated with exponential functions because it describes a situation in which a quantity (the number of transistors) grows at a rate proportional to its size, resulting in exponential growth. Exponential functions are often used to model phenomena in science, engineering, and other fields that exhibit this kind of behavior. In the case of Moore's law, the rate of growth is approximately 41% per year, or a doubling every 1.5 to 2 years. The formula for exponential growth is:
Where:
- y = the final amount
- a = the initial amount
- r = the annual growth rate
- t = the number of years
Moore's law can be expressed using this formula as:
Where:
- N = the number of transistors
- N0 = the initial number of transistors
- t = the time elapsed since the initial observation
- T = the doubling time (approximately 2 years)
For example, if a microchip had 1,000 transistors in 2000, according to Moore's law it would have 2,000 in 2002, 4,000 in 2004, 8,000 in 2006, and so on. The exponential function describes the growth of the number of transistors over time, and the formula allows us to predict future values based on past observations.
~ Zeph